Question about game types.

So I beat the game on normal and was wondering if I could use that 'clear game save' to start hard core or classic or something like that? Is that possible or do I have to start a complete new save file to do those game modes?

I'm always concerned about glitches and computer bugs (Murphy's Law), so as soon as I finished my standard game, I started classic, survival and hardcore games, each on their own separate save file. Now I don't have to worry about losing the ability to
play them. I don't remember the details, but there was something about the process that I thought was a little counterintuitive. Seems like it was select the game mode first and then the save file, as opposed to the other way around.